| Summary: | In this paper, a new relaxation bounding method is proposed for a class of linear multiplicative programs. Although the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>p</mi> <mo>-</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> variable is introduced in the construction of equivalence problem, the branch process of the algorithm is only carried out in <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>-</mo> </mrow> </semantics> </math> </inline-formula>dimensional space. In addition, a super-rectangular reduction technique is also given to greatly improve the convergence rate. Furthermore, we construct an output-space branch-and-bound reduction algorithm based on solving a series of linear programming sub-problems, and prove the convergence and computational complexity of the algorithm. Finally, to verify the feasibility and effectiveness of the algorithm, we carried out a series of numerical experiments and analyzed the advantages and disadvantages of the algorithm by numerical results.
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